Jack and Mary view the same microorganism through the same compound microscope. Mary's near point distance, N_M, is twice as large as Jack's near point distance, N_J. If Mary sees the micro-organism with magnification M_M, the magnification with which Jack sees it is A) 2 M_M. B) M_M /2. C) 4 M_M. D) M_M /4. E) 8 M_M.

Question

Quizplus · Accepted Answer

The magnification of a compound microscope is expressed as the product of the magnification of the objective lens and the eyepiece lens. Let MO and MJ be the magnification of the objective lens for Mary and Jack, respectively, and let ME be the magnification of the eyepiece lens (which is the same for both observers). Then we have:

MS = MO × ME
MJ = MJ × ME

The near point distance is inversely proportional to the magnification of the eyepiece lens, so we have:

NS_M / NS_J = ME_J / ME_M = 2  (given)

Substituting this into the above equations, we get:

MS = MO × 2ME_J
MJ = MJ × ME_J

Dividing the two equations, we get:

MS / MJ = MO / MJ × 2ME_J / ME_J = 2MO / MJ

Therefore, the magnification with which Jack sees the microorganism is half of the magnification with which Mary sees it: MJ = MS / 2. Hence the answer is B.

Jack and Mary View the Same Microorganism Through the Same